{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*LiH dissociation curve using VQE with UCCSD variational form*_\n",
    "\n",
    "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Lithium Hydride (LiH) molecule over a range of inter-atomic distances using VQE and UCCSD. It is compared to the same energies as computed by the NumPyMinimumEigensolver\n",
    "\n",
    "This notebook has been written to use the PYSCF chemistry driver."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pylab\n",
    "\n",
    "from qiskit_nature.second_q.drivers import PySCFDriver\n",
    "from qiskit_nature.second_q.transformers import FreezeCoreTransformer\n",
    "from qiskit_nature.second_q.formats import MoleculeInfo\n",
    "from qiskit_nature.second_q.mappers import ParityMapper\n",
    "from qiskit_nature.second_q.algorithms import GroundStateEigensolver\n",
    "\n",
    "from qiskit_algorithms import NumPyMinimumEigensolver\n",
    "\n",
    "from qiskit_algorithms.optimizers import SLSQP\n",
    "\n",
    "from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD\n",
    "from qiskit_algorithms import VQE\n",
    "from qiskit.primitives import Estimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing step 22 --- complete\n"
     ]
    }
   ],
   "source": [
    "distances  = [x * 0.1  for x in range(6, 20)]\n",
    "distances += [x * 0.25 for x in range(8, 17)]\n",
    "\n",
    "energies = []\n",
    "hf_energies = []\n",
    "estimator = Estimator()\n",
    "\n",
    "print(f'Processing step __', end='')\n",
    "for i, d in enumerate(distances):\n",
    "    print('\\b\\b{:2d}'.format(i), end='', flush=True)\n",
    "    info = MoleculeInfo([\"Li\", \"H\"], [(0.0, 0.0, 0.0), (0.0, 0.0, d)])\n",
    "    driver = PySCFDriver.from_molecule(info, basis=\"sto3g\")\n",
    "    molecule = driver.run()\n",
    "    transformer = FreezeCoreTransformer()\n",
    "    molecule = transformer.transform(molecule)\n",
    "    hamiltonian = molecule.hamiltonian.second_q_op()\n",
    "    mapper = ParityMapper(num_particles=molecule.num_particles)\n",
    "    tapered_mapper = molecule.get_tapered_mapper(mapper)\n",
    "    optimizer = SLSQP(maxiter=10000, ftol=1e-9)\n",
    "    ansatz = UCCSD(\n",
    "        molecule.num_spatial_orbitals,\n",
    "        molecule.num_particles,\n",
    "        tapered_mapper,\n",
    "        initial_state=HartreeFock(\n",
    "            molecule.num_spatial_orbitals,\n",
    "            molecule.num_particles,\n",
    "            tapered_mapper,\n",
    "        ),\n",
    "    )\n",
    "    vqe = VQE(estimator, ansatz, optimizer)\n",
    "    vqe.initial_point = [0] * ansatz.num_parameters\n",
    "    algo = GroundStateEigensolver(tapered_mapper, vqe)\n",
    "    result = algo.solve(molecule)\n",
    "    energies.append(result.total_energies[0])\n",
    "    hf_energies.append(result.hartree_fock_energy)\n",
    "\n",
    "print(' --- complete')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n",
    "pylab.plot(distances, energies, label='VQE')\n",
    "pylab.xlabel('Interatomic distance')\n",
    "pylab.ylabel('Energy')\n",
    "pylab.title('LiH Ground State Energy')\n",
    "pylab.legend(loc='upper right');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum energy: -7.8821399601957 Ha, bond distance: 1.5 Angstrom\n"
     ]
    }
   ],
   "source": [
    "print(f'Minimum energy: {min(energies)} Ha, bond distance: {distances[energies.index(min(energies))]} Angstrom')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qiskit==1.1.0\n",
      "qiskit-aer==0.14.2\n",
      "qiskit-algorithms==0.3.0\n",
      "qiskit-ibm-runtime==0.25.0\n",
      "qiskit-machine-learning==0.7.2\n",
      "qiskit-nature==0.7.2\n",
      "qiskit-nature-pyscf==0.4.0\n",
      "qiskit-qasm3-import==0.5.0\n",
      "qiskit-transpiler-service==0.4.5\n"
     ]
    }
   ],
   "source": [
    "! pip freeze | grep qiskit"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
